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<TITLE>CSE 322 
Assignment 1 
Due Friday, January 5, 1996</TITLE>
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<H1>CSE 322 
Assignment 1 
Due Friday, January 5, 1996</H1>
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<OL><LI> 
Number 20 on page 27.
<LI>
Number 27 on page 27.
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Consider the following ordering of strings in the alphabet <IMG  ALIGN=MIDDLE ALT="" SRC="img1.gif">. This
is called the <em> enumeration ordering of</em> <IMG  ALIGN=MIDDLE ALT="" SRC="img2.gif">.
<P><IMG  ALIGN=BOTTOM ALT="" SRC="img3.gif"><P>
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More generally, strings of length <b>n+1</b> are listed immediately after the
strings of length <b>n</b>.  Those strings of the same length are listed in
alphabetical order. Notice that the rank of the string <IMG  ALIGN=BOTTOM ALT="" SRC="img4.gif"> in the
enumeration ordering of <IMG  ALIGN=MIDDLE ALT="" SRC="img5.gif"> is <IMG  ALIGN=BOTTOM ALT="" SRC="img6.gif">, that is, the rank of 
<IMG  ALIGN=BOTTOM ALT="" SRC="img7.gif"> is <IMG  ALIGN=BOTTOM ALT="" SRC="img8.gif">, the rank of <IMG  ALIGN=BOTTOM ALT="" SRC="img9.gif"> is <IMG  ALIGN=BOTTOM ALT="" SRC="img10.gif">, the rank
of <IMG  ALIGN=BOTTOM ALT="" SRC="img11.gif"> is <IMG  ALIGN=BOTTOM ALT="" SRC="img12.gif">, and so on.
<OL><LI>
Construct as simple a formula as you can for giving the rank of the
string <IMG  ALIGN=BOTTOM ALT="" SRC="img13.gif"> in 
the enumeration ordering of <IMG  ALIGN=MIDDLE ALT="" SRC="img14.gif">.
<LI>
Construct as simple a formula as you can for giving the rank of <IMG  ALIGN=BOTTOM ALT="" SRC="img15.gif">
in the enumeration ordering of <IMG  ALIGN=MIDDLE ALT="" SRC="img16.gif">.
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<P><ADDRESS>
<I>James Fix <BR>
Fri Jan  5 13:13:29 PST 1996</I>
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